When I did further maths at college, we spent a couple of hours on a particular kind of integration, where the function was integrated with respect to the length of the path along the function, typically starting at the point x = 0, y = f(0), and typically calling the path length variable s. I remember that this was curious for all sorts of reasons, but not any specific reason.

It may have been called implicit integration, but googling for that phrase seems to suggest I am remembering it wrong.

I get puzzled looks every time I describe this to people who have studied maths for years for some reason. Does this sound familiar and if so, what's the common name for this?

@TheChaz In that course, the function to be integrated was not a field; more like f(x) = sin(x). Which brings the question of what exactly was integrated; I believe it was the Y of the point.
–
romkynsFeb 14 '12 at 14:22

How about "finding arc length with integration"?
–
The Chaz 2.0Feb 14 '12 at 14:29

@TheChaz Not that. On further thought, I don't think it was the Y that got integrated; that doesn't make much sense. Perhaps the tangent angle relative to that at the starting point?...
–
romkynsFeb 14 '12 at 15:21